TÀI LIỆU DỰ ỨNG LỰC CỦA FIB

Post-tensioning in

buildings

Technical report prepared by

Task Group 1.1

February 2005

Subject to priorities defined by the Steering Committee and the Presidium, the results of fibs work in Commissions and Task Groups are published in a continuously numbered series of technical publications

called 'Bulletins'. The following categories are used:

category minimum approval procedure required prior to publication

Technical Report approved by a Task Group and the Chairpersons of the Commission

State-of-Art Report approved by a Commission

Manual or

Guide (to good practice)

approved by the Steering Committee of fib or its Publication Board

Recommendation approved by the Council of fib Model Code approved by the General Assembly of fib

Any publication not having met the above requirements will be clearly identified as preliminary draft.

This Bulletin N 31 was approved as an fib technical report in March 2004 by fib Task Group 1.1, Design applications, and by fib Commission 1, Structures, in July 2004.

This report was drafted by Working Party 1.1.2, Post-tensioning in buildings, of fib Task Group 1.1:

Joo Almeida (Convener, Instituto Superior Tecnico, Portugal)

Jos Camara (Instituto Superior Tecnico, Portugal), Hugo Corres (ETS de Ingenieros de Caminos, Spain),

Thomas Friedrich (Domostatik Ag, Switzerland), Manfred Miehlbradt (EPF Lausanne, Switzerland),

Jean-Marc Voumard (VSL Switzerland), Bo Westerberg (Tyrns Byggkonsult, Sweden)

Task Group 1.1 members contributing to the report:

Stathis N. Bousias (University of Patras, Greece), Ludovit Fillo (Slovak Technical University, Slovakia),

Stein Atle Haugerud (Olav Olsen a.s., Norway), Toshio Ichihashi (until March 2004, Taisei Corporation,

Japan), Milan Kalny (Pontex s.r.o, Czech Republic), Santiago Perez-Fadon (Ferrovial Agromn,

Spain), Karl-Heinz Reineck (University of Stuttgart, Germany), Jouni Rissanen (Pontek Oy, Finland),

Hiroshi Shiratani (from March 2004, Taisei Corporation, Japan)

Full address details of Task Group members may be found in the fib Directory or through the online services on fib's website, www.fib-international.org.

Cover pictures: ARTS Business and Hotel Centre, Lisbon, Portugal

fdration internationale du bton (fib), 2005

Although the International Federation for Structural Concrete fib - fderation internationale du bton - created from CEB and FIP, does its best to ensure that any information given is accurate, no liability or responsibility of any kind (including liability for negligence) is accepted in this respect by the organisation, its members, servants or agents. All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission. First published in 2005 by the International Federation for Structural Concrete (fib) Post address: Case Postale 88, CH-1015 Lausanne, Switzerland Street address: Federal Institute of Technology Lausanne - EPFL, Section Gnie Civil Tel +41 21 693 2747, Fax +41 21 693 6245, E-mail [email protected], web www.fib-international.org

ISSN 1562-3610

ISBN 2-88394-071-1

Printed by Sprint-Digital-Druck, Stuttgart

fib Bulletin 31: Post-tensioning in buildings iii

Preface

There is no other material than structural concrete that has been the major form-giving

element to the architecture of our time. Although used ubiquitously, expediently, and routinely

throughout the world, it has been rarely used expressively and rarer still beautifully at the hands

of very few gifted individuals.

Its use goes back to the very beginning of civilisation, but it is only since the early part of

the 20th Century that some few ingeniously creative people were able to give it expressive form.

The French engineer, Freyssinet and the Swiss Maillart, whose uniquely memorable bridges span

the vast gorges of that mountainous country, who stand out as the pioneers of concrete design.

Their works have remained as valid structurally as they are visually significant to this day. Pier

Luigi Nervi, the Italian giant of engineering inventiveness, not only in design of concrete, but of

construction method, has not been, in my view, surpassed in giving poetically expressive form to

concrete structures.

Nervi felt intensely what was "correct" structurally; it seemed to be in his blood to "feel"

the rightness of a structural solution, to know the way stresses flowed, to give free reign and

beautiful expression to the laws of nature - not what is "imagined" to be so by many structurally

naive architects - but the unassailable physical truth of statics, based soundly on practical and

ingeniously inventive constructional sense. This is what makes Nervi so unique in this age of

lawlessness and indulgent, irresponsible excesses in architecture and construction. Not only was

he an engineer with a rare gift of poetic expression in the language of structure, but he also was

an experienced - no nonsense - practical contractor-builder.

He not only gave the problems beautiful form, but he also showed us how to build it.

Concrete structures today will vary in different socio-economic locations in the world.

Where manual labour is economically available, concrete structures can be formed to take on

complex geometries, something that is often economically unfeasible in high labour cost

countries with available sophisticated technologies. The speed with which the building must be

erected has a direct effect on the structure and method of construction chosen. The preference in

high labour cost countries is to avoid external scaffolding, for low-rise structures to precast as far

as practical and to prestress concrete, not only horizontally, but also vertically so as to resist

lateral loads.

In most structures today, the increasing use of prestressing has given new freedom to any

concept of forms previously considered uneconomic or unfeasible or unduly bulky to resist

loads. Curvilinear forms have produced an entirely new vocabulary for architecture that in

previous decades would have been thought of as impractical. The use of prestressing has also

been found to be a way of achieving waterproof flat roof surfaces even without the application of

normal bituminous waterproofing, since the concrete is kept in continual compression and resists

cracking which can otherwise lead to water penetration in the long term.

The use of concrete in building is here to stay in our time. It is fireproof, virtually

indestructible and challenges us to devise ever-improved ways of using it with greater economy

in labour, and speed. By constantly absorbing advances in technology it continues to respond to

the demands we place on our new buildings. Concrete helps us in defying gravity in a way that

gives expressive form to the laws of nature.

Prof. Harry Seidler, Australia

iv fib Bulletin 31: Post-tensioning in buildings

Foreword

Working Party WP1.1.3 Post-tensioning in Buildings was established in 1999, integrating

the activities of TG1.1 Design Applications and, more generally, of fib Commission 1 Structures.

The main objective of the Bulletin is to point out the benefits of using post-tensioning for

the more common practical applications in concrete building construction: functional advantages

and architectural freedom, economy, reduced construction time and element dimensions,

improved structural behaviour and quality.

It was the wish of TG1.1 that the document should be addressed mainly to architects,

contractors and owners. Therefore, basic design aspects and design criteria are only summarized,

whereas conceptual design aspects are emphasized.

A set of practical examples, recently constructed buildings, most of them designed by the

WP members, is presented, showing the adopted solutions and their advantages when meeting

the requirements of specific problems. The selected examples were precisely not chosen because

they are outstanding structures. As a matter of fact, post-tensioning principles and technology

can be used in any structure, independently of its importance, covering a wide range of building

structural applications, improving the structure quality and promoting concrete as a structural

material.

The contribution of the Working Party members listed above should be specially

acknowledged. The involvement of all Task Group 1.1 members at the technical discussions,

particularly Milan Kalny, Santiago Prez-Fadon and Karl-Heinz Reineck, is to be mentioned as

well. Finally, WP members express their thanks to Mr. Miguel Loureno and Mrs. Cristina

Ventura for their important contribution to the final editing work.

February 2005

Joo F. Almeida Jean-Franois Klein

Convener of TG 1.1 Chairman of Commission 1

Convener of WP Post-tensioning in Buildings

fib Bulletin 31: Post-tensioning in buildings v

Contents

1 Introduction 1

2 Post-tensioning in buildings

2.1 General 3

2.2 Basic concepts of prestressing 3

(2.2.1 Introduction - 2.2.2 Prestressing in cncrete structures - 2.2.3 Main systems for prestressing)

2.3 Design aspects 8 (2.3.1 Structural effects and tendon profiles - 2.3.2 Prestressing force -

2.3.3 Serviceability limit states (SLS) - 2.3.4 Ultimate limit states - 2.3.5 End anchorage and intermediate anchorages - 2.3.6 Structural restraints)

2.4 Technology of Prestressing in Building 23 (2.4.1 The monostrand post-tensioning system with unbonded greased and sheathed strand

- 2.4.2 The bonded slab post-tensioning system - 2.4.3 Stressing equipment and clearance

- 2.4.4 Installation - 2.4.5 Fire resistance - 2.4.6 Specifications)

Annex: Specification example 39

3 Post-tensioned floors

3.1 Conceptual design 42 (3.1.1 General - 3.1.2 Solid slabs - 3.1.3 Slabs with variable depth)

3.2 Applications 46

(3.2.1 Solid slabs with bonded tendons Fuenlabrada Shopping Center - 3.2.2 Waffle slab with unbond monostrands Alicante OAMI Headquarters - 3.2.3 Parking deck one-

way banded solution GAD Munsten - 3.2.4 Particular applications)

4 Post-tensioned foundations

4.1 Conceptual design 66 (4.1.1 Influence of stiff elements and subgrade friction - 4.1.2 Raft foundations -

4.1.3 Post tensioned slab on ground)

4.2 Applications 70

(4.2.1 Foundation raft P&C Bergisch Gladbach - 4.2.2 Slabs on ground - 4.2.3 Isolated

footing Lisbon St. Gabriel Tower)

5 Post-tensioned transfer slabs and beams

5.1 Conceptual design 85

5.2 Applications 86

(5.2.1 Pacific Place Hong Kong - 5.2.2 Sandwich-Class Housing Development -

5.2.3 Transfer slab Lisbon Eden Hotel - 5.2.4 Transfer beams Funchal Crown Plaza Hotel - 5.2.5 Transfer grid Lisbon St. Gabriel Tower - 5.2.6 Curved transfer beam

School Building-Auditorium Zug)

6 Prefabricated post-tensioned solutions

6.1 Conceptual design 103

6.2 Applications 103 (6.2.1 Prefabricated beams used as scaffolding Printers Bucher-Luzern - 6.2.2 Platform for a Heliport KHIB-Ibbenburen)

fib Bulletin 31: Post-tensioning in buildings 1

1 Introduction

The development of prestressing technology has certainly constituted one of the more

important improvements in the fields of structural engineering and construction. Referring

particularly to post-tensioning applications, it is generally recognized how it opens the possibility

to improve economy, structural behaviour and aesthetic aspects in concrete solutions.

In spite of the simplicity of its basic concepts and well known advantages, the application

extent of post-tensioning solutions can not be considered harmonized in the different areas and

structural applications. In fact, for various reasons, it appears that the potential offered by

prestressing is far from being fully exploited, especially in building structures field. In many

cases in which post-tensioning would provide a visibly superior solution, it happens after all that

a more conventional non-prestressed solution is often selected.

The development of a new building project usually involves the owner, the design team,

where the architect and the structural engineer are included, and, more and more frequently, the

contractor. A survey of practical situations would show that post-tensioning solutions are

frequently not adopted because some of those involved are not familiar with prestressing

technology and its advantages.

It should be pointed out that post-tensioning allows more architectural freedom and can

provide important functional advantages: longer spans providing more flexible solutions,

transition structures solving the conflicts of vertical discontinuities in the building use, and

slender column-free spaces for public areas, are good examples, where post-tensioning is the

right solution.

Concerning economic aspects, the more significant cost in building structures corresponds

to the floor structural system. The use of post-tensioning allows slender and lighter floor systems

with gains on the total building height. Due to the reduction of permanent loads and seismic

action effects, the floor weight influences the size of the vertical elements and foundations. It

should be as well emphasized that the total construction time can in general be substantially

reduced.

The use of prestressing steel can result in a substantial reduction in the total steel area.

Therefore, structural details are improved together with easier placing and compacting of

concrete.

Prestressing offers the possibility of introducing a favourable system of anchorage forces

and tendon deviation forces on the concrete. The transverse components of the anchorage forces

and the tendon deviation forces provide a load balancing system, counteracting the vertical

applied loads, effectively controlling cracking and deformations. The in-plane anchorage forces

precompress the concrete element, leading to higher cracking resistance, improved stiffness and

water tightness, allowing the reduction of expansion joints.

As a conclusion, it can be stated that in many practical situations better technical and

economical solutions can be achieved by using post-tensioning, improving the structure quality

and promoting concrete.

The main objective of the present report is to show the benefits of using post-tensioning for

the more common practical applications in concrete buildings. The document is mainly

addressed to architects, contractors and owners. It is also drafted with the goal of motivating

Copyright fib, all rights reserved. This PDF copy of fib Bulletin 31 is intended for use and/or distribution only by National Member Groups of fib.

2 1 Introduction

building designers to use post-tensioning: basic design aspects related to prestressing effects and

design criteria are summarized and conceptual design aspects are emphasized.

The advantages of using post-tensioning, concerning structural behaviour, economy,

detailing and constructive aspects, are illustrated by the presentation of several existing

structures, most of them designed by Working Party members. General design calculations are

not presented, but design results showing the improvement in structural behaviour illustrated.

References

1.1. FIP Design of post-tensioned slabs and foundations, fib, Thomas Telford, May 1998. 1.2. Ganz, H.R., Advocating a more widespread use of Post-Tensioning, FIP Amsterdam

Congress, Amsterdam, 1997.

1.3. Concrete Society Technical Report N 43, Post-tensioned Concrete Floors Design

Handbook, Concrete Society, London 1994.

1.4. Post-Tensioning in Buildings, VSL International Ltd., Berne, Switzerland, April 1992.



2 Post-tensioning in buildings

2.1 General

Application of prestress in building concrete structures poses no major difficulty in

comparison with any other type of structure. Nevertheless, in some aspects it has its

particularities concerning the type of geometry, loads and/or border constraints. It is the case of

thin slabs, heavy concentrated loads on transition floors or rigid vertical elements that restrain

the prestress effects.

In this chapter the basic structural concepts of prestress are reviewed, the main technology

aspects of prestressing, specially for thin slabs, are presented and the design aspects are

described in a brief way. In what concerns design criteria and calculations the text is oriented to

call attention upon the major issues a structural engineer has to take into account. Simple

calculations are exemplified in order to give the lecturer the order of magnitude of the different

design verifications. Particular aspects of building structures are always referred.

2.2 Basic concepts of prestressing

2.2.1 Introduction

A structural element subjected to bending, e.g. a beam, will carry the load by means of

internal compressive and tensile stresses, see figure 2.1.

Figure 2.1: Compressive and tensile

stresses in a structural element subjected

to bending, e.g. a beam

Compression

Tension

If the material has a low tensile strength, which is the case e.g. for masonry and

unreinforced concrete, the load bearing capacity will be correspondingly low. One way of

compensating for this is to apply a compressive force to the element. This will increase the

stresses on the compressive side and reduce, or even cancel, the tensile stresses, figure 2.2.


4 2 Post-tensioning in buildings

Figure 2.2: Compensating a low

tensile strength by prestressing

with longitudinal compression

Compression

(Tension)

Prestress

In this way a "structure" with no tensile strength at all can act like a beam, e.g. a pack of

books which can be lifted from a shelf by being pressed together, figure 2.3.

Figure 2.3: A pack of books, carrying its own weight

like a beam due to the effect of prestressing

The technique of compensating a low tensile strength by means of compressive forces has

been used for centuries in masonry structures carrying vertical and horizontal forces from arches.

The horizontal forces cause bending in supporting columns. Since the tensile strength of

masonry is low, it was sometimes necessary to add extra weight on the columns, to achieve

sufficient compression for reducing or cancelling the tensile stresses. This is illustrated

schematically in figure 2.4.



Figure 2.4: Example of prestressed columns in a structure with arches

In modern concrete structures, most tensile forces are taken by reinforcement. However, no

significant stress can develop in the reinforcement until the concrete has cracked. This cracking

can often be accepted, but for various reasons it is sometimes desirable to prevent it, or at least

reduce it. Then, again, prestressing can be used. The prestressing is then normally achieved by

means of steel tendons in the form of bars, strands or cables, stressed in tension and thereby

producing a corresponding compression in the concrete. Modern prestressing techniques and the

potential benefits of using them are dealt with in subsequent clauses.

2.2.2 Prestressing in concrete structures

Prestressing is a way of counteracting the effect of external loads on a structure by

imposing a state of stresses contrary to the load effects. The most common way to achieve this is

by means of tendons, which are stressed prior to final loading of the structure.

Prestressing with tendons has two main effects, axial and transverse, see figure 2.5. The

axial effect gives compression in the concrete, caused by anchorage forces at the tendon ends !



figure 2.5 (a, b and c). In case b), the eccentricity of the straight tendon causes bending in

addition to the axial effect. Finally, the use of curved tendons (case c) introduces a transverse

effect that can be designed to more or less counteract the external loads, with both axial, bending

and shear effects.

q

P P

a) Axial effect only

b) Eccentric axial effect

c) Axial and transverse effect

P q P+q

0 0 0

P P

ee

P PT

ensi

on

Co

mp

ress

ion

q

q

Figure 2.5: Illustration of the main effects of prestress. a) represents the pure axial effect. b) represents a typical

pre-tensioned member with eccentric straight tendons, introducing an additional bending effect. c) represents a

typical post-tensioned member with curved tendons, giving axial, bending and shear effects

The transverse effect of prestress will carry a certain part of the external load directly to the

supports. For the remaining load, the structure will have an enhanced resistance to shear,

punching and torsion due to compressive stresses from the axial effect. Prestress will also reduce

deflections under service conditions, due to both the reduced effect of external load and the

increased stiffness caused by delayed or eliminated cracking.

The fundamental and well-known advantages of prestressing can be summarized as the

possibility to limit cracking and deformations in structural members with large spans, to reduce

cross section dimensions for a given span and load and, finally, to increase the load capacity for

given span and dimensions. This is further developed in clause 2.3.

2.2.3 Main systems for prestressing

2.2.3.1 Pre-tensioning and post-tensioning

The two main systems are pre-tensioning and post-tensioning. Although post-tensioning is

the main topic here, the basic features of pre-tensioning will be mentioned for comparison.

With pre-tensioning the reinforcement is prestressed in the mould, before pouring the

concrete. Fixed anchorages for the tendons are needed outside the moulds; therefore the method

is primarily suitable for factory production of precast elements, where several units can be



prestressed with the same tendons in a long line. After sufficient hardening of the concrete, the

prestress is released from the anchorages, and is instead transferred to the elements by bond. For

adequate bond anchorage, tendons have to be rather small; common types are strands " 9 or 13

mm, or single wires. Tendons are usually straight and eccentrically placed, cf. figure 2.5 (b). It is

possible to improve the structural efficiency by introducing a transverse effect from deviation

forces, but this requires deviators fixed into the mould, and is usually avoided for ease of

production.

With post-tensioning the reinforcement is stressed after hardening of the concrete. The

anchorages are fixed into the concrete, and without need for external anchorages the method is

suitable for in-situ construction. Special end anchorages transfer the prestressing forces to the

concrete. This allows larger tendons than in pre-tensioning, since anchorage no longer depends

on bond. Tendons usually consist of several wires or strands with a common anchorage, or of

large diameter bars. Post-tensioning offers great freedom in the layout of tendons for optimum

transverse effect, cf. figure 2.5 (c).

To be stressed after hardening of concrete, tendons must be freely movable in the concrete.

The most common way to achieve this is to enclose them in metal or plastic ducts. After

tensioning, the ducts are filled with cement grout by pressure injection. This has two important

aims: corrosion protection and bond between tendons and surrounding concrete.

Bond is favourable for the structural behaviour, even if tendons are fully end anchored.

However, post-tensioning without bond is also possible. Tendons are then enclosed in plastic

sheaths, with a layer of grease in between, to give corrosion protection and reduce friction.

Unbonded tendons usually consist of single strands. The lack of bond has effects on the

structural behaviour, which must be considered in design.

In most countries, until recently, the most common use of prestressed concrete in buildings

has been in the form of precast pre-tensioned elements, such as hollow core slabs, double-T slabs

and beams of various shapes. Post-tensioning has been used mainly in bridges.

One reason for the limited application of post-tensioning in buildings is that the traditional

systems for post-tensioning have been adapted to bridges, where the need for space, grouting and

heavy stressing equipment is not a major problem. Another reason is that engineers involved in

building design have been unfamiliar with post-tensioning and its potentials.

More recently, however, post-tensioning systems suitable for buildings have been

developed, and post-tensioning is becoming more popular among design engineers. Typical

applications are beams and slabs with large spans and/or heavy loads, particularly flat slabs

where deformations are often a limiting factor.

2.2.3.2 Bonded and unbonded systems

In thin slabs, for obvious reasons, tendons and anchorages must have small dimensions.

Post-tensioning with unbonded tendons then offers some special advantages:

Single strands tightly enclosed in plastic sheaths need less space than multi-strand tendons in ducts with room for grouting. They can therefore be placed closer to the surface.



Large concrete covers are not needed for corrosion protection, since tendons have a built-in protection, and in principle no cover at all is needed for bond. However, conditions for fire

protection are the same as for other reinforcement, and may sometimes govern the cover.

Lighter stressing equipment and the absence of grouting simplifies execution.

Figure 2.6 illustrates the minimum edge distance for unbonded mono-strand tendons and

two types of bonded tendons. For bonded tendons, it is assumed that the minimum cover is 30

mm and not less than the duct diameter. For unbonded tendons the cover can be reduced, e.g. to

20 mm (unless fire protection requires more).

For a slab with h = 280 mm the average eccentricity for the two directions will be for the

cases illustrated in Figure 2.6:

a) e = h/2 t = 140 20 17 = 103 mm

b) e = h/2 t = 140 30 21 3 = 86 mm

c) e = h/2 t = 140 50 50 10 = 30 mm

The disadvantage of bonded tendons with circular ducts is striking. With flat ducts bonded

tendons can be an alternative also in slabs, although they will still be less effective than

unbonded tendons, due to their larger edge distance.

10

Cover 50 mm

Duct 50 mm

4 ! 13

Cover 20 mm

Duct 17 mm

4 ! 13

(c)(a)Cover 30 mm

Duct 21 mm

4 ! 13

(b)

3e e

e

t tt

Figure 2.6: Example of (a) unbonded tendons compared to bonded tendons with (b) flat and (c) circular ducts

respectively

For beams, the disadvantage of reduced eccentricity is normally less pronounced, due to

the greater depth of cross section. Bonded tendons can then be more economical than unbonded

ones, since one tendon then consists of many strands, giving a higher prestressing force per

anchorage.

In the comparison between bonded and unbonded systems, one should also consider the

structural importance of bond, particularly in ultimate limit states. The disadvantages of

unbonded systems from this point of view must be taken into account in design, see clause 2.3.4.

2.3 Design aspects

This clause deals with general design considerations, such as tendon layout and structural

effects of prestress, prestress losses, serviceability and ultimate limit states, anchorages and

restraint from adjacent structural components, with focus on particular aspects for buildings.



2.3.1 Structural effects and tendon profiles

As already outlined in 2.2.2, prestress has two main effects:

The axial effect, causing compression in the concrete, with favourable effects on cracking and deflections and also contributing to shear, torsion and punching resistances.

The transverse effect caused by deviation forces, directly carrying part of the external load to the supports.

With an appropriate tendon layout, the transverse forces can more or less balance part of

the external load. A simple example is shown in figure 2.7. For best efficiency, the tendon curve

should correspond to the bending moment diagram as far as possible. The transverse forces will

then have the same distribution as the external load.

x

e

yPP

q = external load

qP = P.yll due to prestress

q - qP = remaining load

Figure 2.7: The transverse effect of prestress. P = prestressing force, qP = P!y" = transverse load due to prestress, e

= eccentricity of prestressing force, y" = d2y/dx2 = tendon curvature (= constant if y is parabolic, as shown in the

figure)

In continuous members, the minimum curvature required for the tendons will necessitate a

certain distribution of the downward transverse effect over supports. This means that the external

moment diagram cannot be completely followed, see figure 2.8. However, this is not a major

problem as far as the global behaviour is concerned.

qP1

qP1

qP2

Figure 2.8: Example of tendon layout in a continuous member

Normally, tendons are located centrically at simply supported ends. If not, the

eccentricities will give end moments MP = P#e that should be added to the effect of the transverse



load qP, taking into account boundary conditions if the structure is hyperstatic. See figure 2.9.

The effect of the eccentricities can also be seen as the eccentric axial effect mentioned in 2.2.2.

qP1

qP1

qP2

P

e

P

e

Figure 2.9: Effect of end eccentricities

End eccentricities can be used to enhance a certain effect of prestress. Thus, an upward end

eccentricity as shown in figure 2.9 is favourable with regard to shear, whereas a downward end

eccentricity will reduce deflections.

If there are large concentrated loads with fixed position, the tendons can be bent in a

concentrated curvature at these positions, and be more or less straight in between. This gives

concentrated lifting forces to directly balance (part of) the external loads, see figure 2.10.

Figure 2.10: Tendon layout with straight

parts, in this case to balance

concentrated loads

A tendon layout with straight parts is sometimes used also for practical reasons, even if

there are no concentrated loads. Parts of the tendons can then be supported directly on the bottom

reinforcement, which simplifies execution, especially in slabs.

2.3.2 Prestressing force

2.3.2.1 Maximum prestress

The maximum prestress is limited to values, which are given in codes. As an example the

following stress values can be mentioned:

Maximum stress during tensioning: #p $ 0,90#fyk and $ 0,80#fuk

Maximum stress after tensioning and anchoring: #p $ 0,85#fyk and $ 0,75#fuk

Here fyk and fuk are the characteristic values of yield and ultimate tensile strength

respectively. For common types of strands, the maximum stresses will be around 1500 and 1400

MPa respectively.

The effect of the total prestressing force on the concrete may impose other limits on the

maximum prestress.



2.3.2.2 Losses of prestress

The prestressing force applied at the anchorage will decrease along the tendon length, and

also with time. These so-called losses of prestress are of the following main types:

a) Losses due to elastic shortening of concrete b) Losses due to friction along the tendon c) Losses at the anchorage zone due to wedge draw-in d) Time-dependent losses due to material properties of concrete and steel

The different types of losses will be described in the following, with special emphasis on

friction and time-dependent losses.

a) Elastic shortening of concrete

During tensioning the concrete is subjected to compression and a corresponding

shortening. If there are several tendons which can not be tensioned at the same time, the force in

tendons already tensioned will decrease each time another tendon is tensioned.

The average loss can be related to half the total prestress. The concrete shortening $c and

the corresponding loss of prestress %#cp is then:

$c & 0,5P / (AcEc) = 0,5#c/Ec %#p = Es#$c = 0,5(Es/Ec)##c & 3#c

(P = total prestressing force, Ac = concrete area, #c = P/Ac, Ec and Es = E-modulus of

concrete and steel respectively; normally, Es/Ec & 6)

For post-tensioned slabs in buildings, where typically #c & 1,5 MPa, the loss will be about

5 MPa, which is quite negligible. For beams and certain types of bridges, prestress may be 5

times as high and the corresponding loss then about 25 MPa; this is still not very much.

b) Friction

The prestressing force decreases with increased distance from the active end due to

friction. The variation of the force then follows from

Px = P0#e- '#(% + k#x)

where

P0 prestressing force at the active end

coefficient of friction

&% sum of angular deviations over distance x (absolute value)

k unintentional angular deviation per unit length

x distance from the active end to the section considered

The distance x should in principle be measured along the tendon, but a straight length

coordinate can normally be used. The reduction of the prestressing force over a distance x is

%P = P0#[1 - e-#('% + k#x)] & P0##('% + k#x)

The values of can vary substantially, but there is a fundamental difference between

unbonded and bonded tendons. The following values can be taken as indications:



1) 0,05 for unbonded tendons 2) 0,15 for bonded tendons in plastic sheathing 3) 0,20 for bonded tendons in metal sheathing

In the simplest case, a simply supported beam or slab with parabolically varying

eccentricity of tendons, the prestressing force will vary practically linearly from one end to the

other, see figure 2.11.

Figure 2.11: Example of

variation of prestress due

to friction

x

e

P1P0

P0 P

1P

m

l

Example

Compare unbonded and bonded tendons with the friction values indicated above.

l = 10 m, e = 0,2 m. In the middle, % = 4e/l = 4#0,2/10 = 0,08 rad. Assume k = 0,01.

1) = 0,05 ( Pm = P0#e-0,05#(0,08 + 0,01#5)

= 0,994#P0 ( friction loss = 0,6 % of P0

2) = 0,15 ( Pm = P0#e-0,15#(0,08 + 0,01#5)

= 0,981#P0 ( friction loss = 1,9 %

3) = 0,20 ( Pm = P0#e-0,20#(0,08 + 0,01#5)

= 0,974#P0 ( friction loss = 2,6 %

For cable layouts of continuous members these losses are naturally bigger and would, in

normal situations, amount to values of the order of 5% to 20%.

c) Wedge draw-in

When tendons are locked in the anchorage, a certain displacement (draw-in) occurs before

the wedges have full grip, see figure 2.12. This causes a reduction of the prestressing force,

which can be calculated if the magnitude of the draw-in is known (this is usually stated in the

technical specifications for a certain system).



Figure 2.12: Wedge draw-in

!

Figure 2.13 shows the variation of the prestressing force before and after wedge draw-in

(exaggerated), and for the cases of normal length and short tendons.

Before

After

!p0

!p"

!px#!

p

Before

After

!p0

!p"

#!p

x

l

l

x

a) x < l b) x > l

Figure 2.13: Variation of prestress before and after wedge draw-in for a normal length and a short tendon

respectively

In case a) we have

2s

p x

E!

"=

#$ ' = wedge draw-in

(#p = #p0 - #p' & 2!#p0! (% + kx) = 2!#p0!)!x ) = (% / x + k) = average relative

friction loss per unit length

p0/ !"#=x and p00pp /2 !"#$$ %=& $p0 = #p0/Es = initial prestrain

In case b), which occurs if the resulting x is greater than l, the following value of the loss at

the active end can be derived:

%#p = Es#' / l + #p0#)#l



Example

l = 10 m, e = 0,2 m (parabolic), k = 0,01, ' = 6 mm, #p0 = 1000 MPa ( $p0 = 0,005

Parabola ( % /x = 8e/l2 and ) = #(% /x + k) = 0,05#(8#0,2/102 + 0,01) = 0,0013

x = ( )0 006 0 0013 0 005, / , ,! = 30 m.

Since x > l we have case b):

%#p = Es#'/l + #p0#)l = 200000#0,006/10 + 1000#0,0013#10 = 120 + 13 = 133 MPa

d) Time-dependent losses

The prestress will decrease with time due to shrinkage and creep in the concrete, plus

relaxation of the tendons. Different expressions for the time-dependent loss can be found in

codes. However, the basic expression is always

sp

c

cp

scssp !""

#$" ++=%E

EE

where

Es E-modulus of steel

Ec E-modulus of concrete

$cs shrinkage of concrete

* creep coefficient of concrete (creep = strain increase under constant stress)

#cp concrete compressive stress at level of tendons for quasi-permanent load

+ relative relaxation loss (relaxation = stress decrease under constant strain)

#sp stress in tendons

The physical meaning of the basic expression is simple: the first two terms express the

stress decrease due to concrete shortening from shrinkage and creep respectively, the third term

expresses the stress decrease due to prestress steel relaxation, given by the coefficient ).

The concrete stress #cp should be evaluated for the quasi-permanent (long-term) load

combination together with prestress.

Example

#p0 = 1340, #cp = 3 MPa; Ep = 200, Ec = 30 GPa; $cs = 0,0003, * = 2,5, + = 0,03

Shrinkage: %#ps = Es#$cs = 200#103#0,30#10-3 = 60 MPa

Creep: %#pc & (Ep/Ec)#*##cp = (200/30)#2,5#3 = 50 MPa

Relaxation: %#pr & 0,03#1340 = 40 MPa

%#p = 60 + 50 + 40 = 150 MPa

%#p/#p0 = 150/1340 = 0,11 = 11 %

This is a typical value; time-dependent losses are generally between 10 and 15 %.



2.3.3 Serviceability limit states (SLS)

The governing design criteria for prestressed structures are normally those relating to

service conditions, the so-called serviceability limit states (SLS). The reason for choosing

prestressed concrete is often a large span and/or a requirement on reduced depth, leading to a

high span-depth ratio. In such cases, deflections often become critical.

If concrete is uncracked, the deflection (see figure 2.14) can be expressed in the following

general way:

3

3

3

2

4

1

4

1

!"

#$%

&=

'==

h

l

bE

qk

l

a

bhkE

qlk

EI

qlka

where

q distributed load

l span length

E concrete modulus of elasticity

I moment of inertia of cross section

k1 coefficient depending on load distribution and boundary conditions

k2 coefficient depending on cross section geometry

k3 k1/k2

b width of cross section

h depth of cross section

a

h

q

l

Figure 2.14: Illustration of deflection a, length l, depth h and load q

The above expressions shows that the absolute deflection a is proportional to l4 and the

relative deflection a/l is proportional to (l/h)3. This illustrates the strong influence on

deformability of the span length and the span-depth ratio.

Prestress can be designed so that the deformation under a certain load, e.g. permanent or

quasi-permanent, is partially or totally balanced by the transverse effect. In this way

deformations can be kept within acceptable limits.

However, there are limits to the possible slenderness with regard to economy and structural

behaviour: excessive quantities of prestressing steel should be avoided and the structure should

have sufficient stiffness for variable loads, sometimes also with regard to vibrations.



In the final deformation calculation, concrete creep has to be taken into account. The

additional deflection due to concrete creep is, provided the structural member is uncracked:

)(5,2)( P0g0P0g0creep!"!" +#+$= aaaaa %

where

* creep coefficient, see below !

g0a downward deflection due to quasi-permanent load

!

P0a upward deflection due to transverse effect of prestress

The creep coefficient * depends on concrete composition and quality, ambient humidity

etc. Values 2 and 3 are typical for outdoor and indoor conditions respectively. Thus, due to creep

the total deflection may become 3 to 4 times the immediate (elastic) deflection.

The limits for acceptable deflections depend on the type of structures. They are generally

not stated in much detail in codes, instead they must often be specified by the client. For large

spans and/or span-depth ratios, it is often impossible to fulfil the deformation requirements

without prestress. In the specification of deflection limits, different criteria and different types of

deflection must be considered. For example, additional deflections have implications with regard

to damage to non-structural building components, total deflections have implications with regard

to function and appearance, initial deflections can be compensated by pre-camber, etc.

Therefore, a specification like deflection not greater than span/500 or similar is too vague. It

must also be stated whether a limit concerns immediate, additional or total deflections, and to

which load combination it applies.

With regard to deflections and other serviceability criteria, the slenderness l/h of

prestressed members can be up to 1,5 to 2 times that of reinforced concrete members. The

prestressing is generally designed for a transverse effect corresponding to about 70 to 90% of

permanent or quasi-permanent loads. With such prestress, crack control is generally not a major

issue, since there will be compression or only small local tension under quasi-permanent load.

Cracks as such are generally not a problem in normal buildings, but cracking may have a

significant effect on deflections, and may therefore have to be avoided or limited in frequent or

rare load combinations. Cracks may also be undesirable with regard to appearance.

With regard to the possibility of cracking under a high variable load, or due to imposed

deformations (sometimes not foreseen in design), minimum reinforcement should in general be

provided for crack control. Minimum amounts of reinforcement are generally well-defined in

modern codes of practice.

2.3.4 Ultimate limit states

For load bearing structures it is not sufficient to limit deflections, cracks and stresses in

SLS. To ensure a certain safety margin against failure or collapse, also the so-called ultimate

limit states (ULS) have to be considered. All possible failure modes should be considered, e.g.

bending, shear, punching, torsion, anchorage of reinforcement and prestressing tendons, etc.



Design models and criteria for ULS verifications are generally treated in sufficient detail in

codes. Therefore, in this document only some particular aspects will be treated, especially those

related to the effects of prestress. These effects can be considered in different ways: as an

imposed deformation, an equivalent load or a contribution to resistance. Apart from that, certain

types of resistances are improved due to the axial effect of prestress: shear, torsion, punching. In

design verifications it is important to consider these different effects in a consistent way, so that

no single effect is taken into account more than once.

Concerning the bending resistance, a major advantage of prestressing is that steel with

very high strength can be used. Without prestress, the utilisation of high steel stresses will lead to

excessive deflections and cracking in SLS. With a high strength, 3 to 4 times that of ordinary

reinforcement, the steel area necessary to achieve a certain bending resistance can be reduced

proportionally. This, together with the possibility of grouping several strands in few tendons,

clearly facilitates the detailing of the tension zone.

The ultimate bending resistance is

MRd = FT # z

where FT is the total tensile force and z is the internal lever arm, see figure 2.15. The

tensile force FT is approximately given by

FT = As fyd + Ap fpd for bonded tendons (1)

FT = As fyd + P + Ap %#p for unbonded tendons (2)

where

fyd design strength of ordinary reinforcement

fpd design strength of prestressing tendons

P = Ap #p prestress stress force

# p prestress stress

%# p & 100 MPa stress increase above prestress for unbonded tendons

Figure 2.15: Examples of stresses and

forces in a prestressed concrete

section for the ultimate limit state of

bending

Ap

As

Ap

fpd

or

P + Ap!"

p

As fyd

FT

FC

z

Bonded tendons (1) are locally elongated at cracks. This gives a higher strain and a

correspondingly high stress increase, whereby the total strength of the total steel can be utilized.

(

(1) (

(2)



Unbonded tendons (2) are instead elongated uniformly between the anchorages. This may

involve several spans in a continuous beam or slab. As a consequence, the strain and the

corresponding stress increase at failure is limited, often leaving the total stress below yielding,

even with extensive cracking. The value 100 MPa is a rough estimate of the stress increase,

which can be used in the absence of a detailed calculation. In such a calculation, the global

structural deformation has to be considered, including possible restrictions with regard to plastic

rotation capacities.1

Example

The ultimate bending capacities are compared for a cross section with (1) bonded and (2)

unbonded tendons and the following data: As = 1256 mm2 (4*20); Ap = 2100 mm2 (2 tendons,

each with 7 strands at 150 mm2); #p = 1050 MPa; fpd = 1680/1,15 = 1460 MPa; fyd = 500/1,15 =

435 MPa, z = 1,25m.

(1) MRd = 10-3#[1256#435 + 2100#1460]#1,25 = (546 + 3066)#1,25 = 4515 kNm

(2) MRd = 10-3#[1256#435 + (1050+100)#2100]#1,25 = (546 + 2415)#1,25 = 3700 kNm

Thus, in this case only 80 % of the potential capacity can be used if tendons are unbonded.

Shear resistance

With curved tendons, the main contribution of prestress to the shear resistance is normally

given by the inclination of tendons, as illustrated in figure 2.16, i.e. the transverse effect of

prestress. The contribution to the shear resistance is simply the transverse component of the

prestressing force. Using a so-called truss model for the design of shear reinforcement, and with

prestress considered on the action side, the design criterion is:

!tan SdRdsy PVV "#

where cotydsw

Rdsy !""= zfs

AV resistance of shear reinforcement, see figure 2.16.

Alternatively, with prestress considered as a contribution to the resistance:

SdRdsyRd tan VPVV !+= "

Thus, the only difference is whether the contribution of inclined tendons is placed on the

right or left hand side of the design equation.

1 The lack of bond also has other implications. Thus, a local failure will have consequences along the whole length

between anchorages, and in a continuous member several spans may suffer from loss of prestress. This should be

considered particularly with regard to accidental actions and unintentional cutting of tendons for openings. (In the

case of planned cuttings, it is possible to install new anchorages in existing tendons.)



!

aP

Asw

fyd

z

VSd

s

z.cot!

Figure 2.16: Shear ultimate limit state of a prestressed concrete element

Example

d = 1,4 m; z & 0,9d = 1,26 m; Asw/s = 1050 mm2/m (stirrups *10s150); Ap = 2100 mm2;

P=2200kN; tan, = 0,1; cot% = 2 (% & 26 = inclination of compression struts in truss)

VRd = 2200#0,1 + 10-3#1050#435#1,26#2 = 220 + 1150 = 1370 kN

The axial effect of prestress also has an effect on the shear resistance, particularly for

members without shear reinforcement. For members with shear reinforcement, the contribution

from the axial effect will be different depending on which design model is used. In the truss

model, the axial effect of prestress is generally small, often zero. In other models (e.g. addition

model or modified compression field theory) this effect can be more significant. However, the

effect of inclination as shown above is the same for all models.

In punching of slabs the effect of prestress is similar, but only tendons close to the column

can be taken into account. Figure 2.17 gives an indication of which tendons can be taken into

account; the distances x and y can be found in some codes being x generally limited to d/2. The

axial effect of prestress is favourable also in punching, but less than in shear. It also depends on

the problem of prestress disappearing into adjacent members, see paragraph 2.3.6.

Figure 2.17: Tendons contributing to the

punching resistance in slabs

x

x

a a + 2x

d

yy

a

a

PP

b



2.3.5 End anchorage and intermediate anchorages

The prestressing force is transferred to the concrete at the anchorages. Anchorages where

stressing takes place are called active anchorages, whereas the others are called passive.

Sometimes stressing is made from both ends of a tendon to reduce friction losses.

Where tendons cross a construction joint, intermediate anchorages can be placed. After

hardening of the concrete in the first pour, the tendons are stressed and locked. The tendons in

the next pour are connected to the ones already stressed, and stressed after hardening of this

concrete. It is not necessary to have intermediate anchorages in all construction joints, or in all

tendons in one joint; tensioning can also be postponed to subsequent joints.

At the anchorages, a complex state of stresses is generated. Two aspects deserve special

attention: high local compressive stresses at the anchorages, and tensile stresses caused by the

dispersion of the compressive stresses over a larger area. The compressive stresses must be

limited, and the tensile stresses normally have to be equilibrated by reinforcement. Figure 2.18

illustrates these two aspects, particularly how to take care of the tension. The tension is taken by

reinforcement, and the compression is limited with regard to the concrete strength at the time of

tensioning.

Figure 2.18: Distribution

of stress at an anchorage

zone and typical detailing

NN / 2

N / 2

TensionCompression

Ties (tension)Struts (compression)

Stress trajectories Simplified model

In the detailing of prestressing solutions in buildings, the geometry of anchorage zones

may have to be designed in order not to interfere with architectural and functional needs.

2.3.6 Structural restraints

In long structures, joints may be needed to allow movements due to prestressing, shrinkage

and temperature changes. The axial effect of prestress produces immediate elastic shortening of

the concrete, later increased by creep. Shrinkage always occurs, whereas significant temperature

changes mainly occur in outdoor structures. Examples of the magnitude of different types of

movements are given below:

Movement in mm/m

Nordic countries Mediterranean countries

Outdoors Indoors Outdoors Indoors

Prestress 0,15 0,20 0,20 0,20

Shrinkage 0,25 0,40 0,30 0,30

Temperature 0,40 0,00 0,30 0,10

Total 0,80 0,60 0,80 0,60



The example is based on a prestress of 1,5 MPa in the concrete. The following has been

assumed for both regions (outdoors / indoors respectively): creep coefficient 2 / 3, shrinkage

0,25 / 0,4 o/oo. The temperature decrease has been assumed to 40 / 0 for Nordic and 30 / 10 for

Mediterranean countries. The values given are only indications, not general recommendations.

Due to the axial effect of prestress, the need for movement joints is more pronounced in a

prestressed floor than in the same floor without prestress. The need is also generally more

pronounced with post-tensioned cast in situ floors than with pre-tensioned precast elements. In

these last elements, all the elastic shortening plus part of the creep and shrinkage has occurred

before assembly, furthermore there is no prestress in the transverse direction and movements can

be distributed between the many joints.

The need for movement joints depends not only on the dimensions of the building, the type

of floor etc, but also on the layout of the stabilizing system. Some schematic examples are shown

in figure 2.19 to illustrate this.

In examples a), b) and c) there will be no significant forces due to restraint, since the

stabilizing walls have a low out-of-plane stiffness. On the other hand, the unrestrained

movements may have effects on non-structural parts of the building, such as windows, partitions

etc.

In examples d) and e) the restraint forces may become significant, particularly if the floor

is post-tensioned in the longitudinal direction of the building. It may be necessary to arrange

some possibility for movement, either between the floor and one of the stabilizing units, or in the

floor itself. The second alternative may require additional stabilization, since the joint will

interrupt the stiffness and bending capacity of the floor diaphragm. Without joints, various

aspects of restraint have to be taken into account in design, among other things a reduction of the

axial effect of prestress. This will be further discussed below.

In cases like d) and e), the effects of restraint should be analysed, taking into account the

magnitude of unrestrained movements (cf. example above), the stiffness of floor and restraining

structural components, favourable effects of concrete relaxation and cracking, etc.

The effects of shortening and restraint described above also have another aspect, namely

that part of the prestress may disappear into adjacent members, which are not primarily

intended to be prestressed. This means that the axial effect is reduced in the prestressed member,

and this must be taken into account in design. It may also have undesirable effects on the

adjacent members concerned.



L

a)

No significant restraint

Max. movement - prop. to L/2

b)


Max. movements - prop. to L

c)


Max. movement - prop. to L

d)

Significant restraint forces

Small movements

e)

Significant restraint forces

Small movements

Figure 2.19: Examples of stabilizing systems and their effect with regard to restraint

A typical example is a floor supported on walls, as is often the case with underground and

bottom floors, see figure 2.20. Cracks as indicated may occur in the floor due to restraint from

the walls. The cracks are not necessarily a major problem as such (if appropriate minimum

reinforcement is provided), but they may give an uneven distribution of the axial effect of

prestress in the floor, due to arch action. In this particular example it would reduce the

compressive stress on the central zone of the floor, where in this example it could be particularly

useful with regard to the punching resistance.



Figure 2.20: Shortening and cracks in floor due to prestress and restraint from walls

The problem can be avoided by reducing restraint through movement joints, or by

prestressing also the walls. In the latter alternative the movements in the walls could be made

similar to those of the floor, but the result could also be that the problem is moved to some other

part of the building, e.g. the connection of the wall to a rigid foundation.

It should be kept in mind that, wherever the axial effects of the prestress end up, the

transverse effects will always act fully on the prestressed member, and can be accounted for in

every aspect of design.

2.4 Technology of prestressing in building

This section illustrates some examples of post-tensioning systems currently used in

building construction.

2.4.1 The monostrand post-tensioning system with unbonded greased and sheathed strand

For thin construction elements such as slabs in building, the monostrand post-tensioning

system was developed to suit efficient construction methods. These light, flexible monostrands

can be easily and rapidly installed and as there is no grouting can lead to economical solutions.

Each end of the strand is anchored in an individual anchorage device.

Components:

The following types of anchorage are available: stressing anchorage, dead end anchorage

and coupler.



D Couplers (at construction joints)

B Stressing AnchorageC Dead End Anchorage

Stressing Equipement and Clearence

A The Monostrand

Figure 2.21: Schematic layout of the mono-strand post-tensioning system

A The monostrand

Plastic sheath

t=1mmStrand

Permanent corrosion

preventing grease

Figure 2.22: Structure of the monostrand

The monostrand is a 7-wire strand of patented cold-drawn twisted wires which have been

stress-relieved or stabilised. In the factory or workshop, the strand is first given a continuous

coating of permanent corrosion preventive grease and then a plastic sheath of either polyethylene

or polypropylene is extruded or pushed over the greased strand.

The quality and dimensions of the materials vary from one country to another and therefore

careful attention should be given to the criteria and codes (EN 10138-1, BS 5896 or ASTM

A416). It is believed the EN standard, which combines the specifications of the materials

certified in the member states of CEN (Comit Europen de Normalisation), will soon become

the common standard.

Figure 2.23: Views of monostrand bundles at anchorage and over support. Monostrands can be supplied from the

workshop already bundled and placed in this form. A monostrand bundle may comprise a group of 2, 3 or at most 4

strands



Recommended design values:

Spacing of tendon supports 0.6 to 1.5 m Minimal radius 2.5 m Friction coefficient = 0.06

Unintentional angular deviation per unit length k=*(, = 0.0005 m-1

Corrosion protection

The corrosion protection should be in accordance with fib or PTI recommendations. The

plastic sheathing (PE or PP) forms the primary protection of the monostrand and the corrosion

preventive grease the secondary protection.

Special product

Internal Unbonded Tendons

Figure 2.24: Tendons connected by webs to a flat band (VT-CMM-System)

B Stressing anchorage

The components of the stressing anchorages are the anchorage body of cast steel (sprayed

at the workshop with a corrosion preventive oil) with wedges, a polyethylene sealing sleeve and

the recess former. The fixation of the stressing anchorage is done by setting out and marking of

cable axes on stop-end formwork, drilling a hole " 30 - 35 mm for passage of the recess former

fastener, then fastening the recess former to the stop end with the lock nut.

Figure 2.25: Anchorage elements

Projecting length Recess form

Anchorage bodyJastener

Lock nutWedge PE-Sleeve

or connectorGreased and coated

strand



Corrosion protection:

The corrosion protection of the strand portion and wedges in the anchorage body is critical.

The internal cavity of the anchorage body is therefore injected under pressure with permanent

corrosion protective grease and closed by a grease-filled PE-protective cap.

The plastic sealing sleeve, which is pushed or screwed on the transition pipe of the

anchorage body, seals the transition zone between anchorage body and PE strand sheath. To

protect the anchorage body from external influences, the block-out is afterwards carefully packed

with mortar.

Figure 2.26: System with enhanced corrosion protective properties

C Dead end anchorage

The dead end anchorage is identical in appearance to the stressing anchorage. It is usually

fitted onto the tendon at the workshop. The wedges are pressed in and secured against backwards

movement.

Figure 2.27: Anchorage elements

!30

Anchorage body (casting)

PE-Sleeve

Closure Cap




Once again, the cavities in the anchorage are injected with a corrosion preventive grease

and the anchorage body is sealed with the closure plug. The plastic sealing sleeve seals the

transition zone between anchorage body and PE strand sheath.

The dead end anchorage is fixed to the formwork in such a manner that, once concreted,

there is sufficient concrete cover to protect the anchorage permanently against external

influences. Other systems with a lower degree of protection consist in a dead end casting

combined with compression fitting.

D Couplers

As extensive floor areas are subdivided into smaller manageable pouring stages and post-

tensioned in sections, the cables at the construction point are connected with couplers to the

cables that have been already stressed.

All the couplers are practically based on the same concept and consist of a coupling body

with coupling head and threaded coupling.

The coupling head is screwed in the coupling body of the stressed cable. The strand is then

inserted into the self-gripping locking device of the coupling head.

Figure 2.28: Coupler elements


The corrosion protection is the same as for stressing anchorage with the coupling being

injected with a permanent corrosion protection grease. Setting a sleeve coated with grease over

the coupling head completes the corrosion protection. Aside from the usual method of protection,

some systems with additional special protection in the sleeve between the end of the plastic

sheath of the monostrand and the anchor head can be found.

2.4.2 The bonded slab post-tensioning system

As an alternative to the unbonded monostrand, the bonded post-tensioning system is also

particularly suitable for thin construction elements in building and bridges such as transverse

deck slab pre-stressing. Due to the flat profile of the duct, the static depth can be more efficiently

utilised and the cable eccentricity improved in comparison to a round duct for the same number

of strands.

Each strand end is anchored either in an individual anchorage device (monostrand) or more

often in a common anchor for up to 5 strands contained in flat-shaped ducting and anchorages.

Stage 1Stage 2

PE-Sleeve in

two parts Coupling headThreaded coupling

Coupling body

PE-Sleeve

Monostrand 1Monostrand 2Construction joint



Strands are individually stressed and gripped by the normal wedge action. After stressing the

duct is injected with a cementicious grout, which bonds the strands to the surrounding concrete.

As a result of the bonding, the stressed tendon has a higher capacity at ultimate design.

2.4.2.1 The monostrand system

In case of bonded monostrand tendons, a corrugated metal or plastic conduit is used, which

is grouted after completion of the stressing operation.

A special transition piece (grout connector or grout pipe) allows for grouting.

Figure 2.29: Elements of the bonded monostrand tendon

2.4.2.2 The multistrand system

Components:

The following types of anchorage are available: stressing anchorage, dead end anchorage

and coupler.

D Couplers (at construction joint)

C Dead End Anchorage

A Flat Duct Stressing Equipment and Clearance

B Stressing Anchorage

Figure 2.30: Schematic layout of the multistrand post-tensioning system

Bare strandFlexlible conduit

WedgeGrout pipe

Grout connector

Protection cap



A Flat duct

Tendons in standard corrugated steel flat ducts


Spacing of tendon support 0.8 to 1.0 m

Minimal radius 2.5 m (vertical)

6.0 m (horizontal)

Friction coefficient =0.2

Unintentional angular deviation per unit length k= *(, = 0.0008

Figure 2.31: Steel flat ducts

Tendons in corrugated polyethylene or polypropylene ducts


Spacing of tendon support

Minimal radius 2.5 m (vertical)

6.0 m (horizontal)

Friction coefficient = 0.14

Unintentional angular deviation per unit length k=*(, = 0.0010

H =21 mmB= 75 mm

Flat steel duct

H

B

Cement grout

Bare strands



Figure 2.32: Polyethylene flat ducts(PT-Plus TM

)

B Stressing anchorage

Anchorages for flat duct system can be differentiated in three groups:

One piece comprising of both bearing plate and anchor head, which is installed into a

block-out after concreting; the four strands, which lie alongside one another in the flat tendon are

individually threaded through the anchorage and stressed. After concreting, the reusable block-

out form is removed with the end formwork.

Figure 2.33: Components of a stressing anchorage of group 1

H =35 mmB= 86 mm H

B

Cement groutPlastic duct

Bare strands



Figure 2.34: Stressing anchorage of group 1

One piece comprising of both bearing casting and anchor head where the casting is

installed in the same way as a casting for the multi-strand system

Grout inlets

Flat sleeve

Flat duct




Two pieces with a casting and an anchor block allowing the stressing of 4 or 5 strands.


Corrosion protection

The demands for construction quality and durability have been increased leading to the

requirement for systems with a higher performance level. Each of the strands is placed within a

corrosion-resistant polypropylene duct. Positive duct-to-anchorage connections provide full

strand encapsulation, leaving no partial strand lengths exposed to the surrounding concrete.

The strand encapsulation is maintained even at slab construction joints by the incorporation

of improved system details.

Figure 2.37: Stressing anchorage with enhanced corrosion protection (VSLAB TM

)



C Dead-end anchorage

Where high level of corrosion protection are required and a need for the pre-stressing force

to be transferred as near as possible to the end of a structural component, the stressing anchorage

can be used as dead end anchorage.

Where the pre-stressing force must only be transferred as near as possible to the end, an

anchorage with retainer plates and compression fitting can be used.

Figure 2.38: Elements for dead end anchorage with bearing plate

In other cases, the pre-stressing force can be transferred by the bonding of the bare strand

and partly by direct bearing of the bulb at the end of the strands.

Figure 2.39: Elements for dead end anchorage by bond

A third not so usual dead end anchorage is the loop anchorage where the strands form a

loop around a bent plate. The force is transferred through the bonding of the strands and the

pressure onto the plate.



D Couplers

The couplers enable a new cable to be connected onto a previously installed and stressed

cable. Different degrees of corrosion protection can be achieved:

high degree of corrosion protection with fully encapsulated strands

Figure 2.40: Components of a coupler with high degree of corrosion protection. (VSLAB TM

)

Figure 2.41: Other example of coupler

ClampHalf-shell

Form work

Coupler bodyTrumpet

Clamp Half shell

PT-PLUS Duct

GasketGrout tube

Trumpet



lower degree of corrosion protection where the strands are exposed to the surrounding

concrete.

Figure 2.42: Coupler elements with lower degree of corrosion protection

2.4.3 Stressing equipment and clearance

In normal case, the stressing of the strands for post-tensioning in buildings is done with a

front-gripping hollow piston jack with a stroke of 200 mm and a weight of approximately 20 kg.

Figure 2.43: View of the front-gripping hollow piston jack and some characteristics

19

5

790116

Stroke : 200 mm 300 mm

Capacity : 230 kN 300 kN

Weight : 23 26 kg



In special cases such as short clearances (block-outs) or exceptionally for intermediate

anchorage with continuous strands, the twin ram jack will be used with a special chair for

stressing.

Figure 2.44: View of the twin ram jack and some characteristics

Jacking systems with two to four strands have been developed.

Figure 2.45: Systems with two and four strands

For further information, consult system catalogues. The jack clearance requirement can be

assumed as follows:

A

B

C

Centre hole jack Twin ram jack

A [mm]

B [mm] 2 strand jack 2 strand jack 4 strand jack

C [mm] rectangular anchor

4 strands 5 strands

square or circular anchor 1 strand

2 strands 4 strands

950 - 1100

70 - 90 110 130

280 400

70

105 115

700 - 1200 60 - 80

- -

300

400

- - -

Table 2.1: Clearance for jacks

The dimensions of internal stressing pockets or recess depend on the above values and may

vary for particular applications.

163 600

24

0250

190

VT Vorspann - Technik 600X250

Weight : 20 30 kg

615

Stroke : 200 mm 250 mm

Capacity : 230 kN 290 kN

240

165

84



Space requirements

The average distances to concrete edges and adjacent anchorages are given in the

following tables as a first approximation. For final value, refer to the agreements.

Monostrand post-tensioning

Xr X

Y

Yr

13 mm 340 190 160 100 240x100

X Xr Y YrAnchor

dim.

Strand

type

120200210 265x13039015 mm

[mm]

XXr

Y Yr

X

15 mm 160 105x75100 110 75

[mm]

100

Strand

type

13 mm

XrX

150 90

Anchor

dim.YrY

70 110x70

Table 2.2: Space requirement for monostrand post-tensioning (average values)

Bonded slab post tensioning

Xr X

Y

Yr

13 mm 340 190 160 100 240x100

X Xr Y YrAnchor

dim.

Strand

type

120200210 265x13039015 mm

[mm]

XXr

Y Yr

X

15 mm 160 105x75100 110 75

[mm]

100

Strand

type

13 mm

XrX

150 90

Anchor

dim.YrY

70 110x70

Table 2.3: Space requirements for bonded slab post-tensioning (average values)

2.4.4 Installation

Unbonded monostrand system

Reeling chair with drive motor for coiling individual cables in the factory and transporting

individual cables coils. Transport palette up to 2.5 to bundles of tendons.

Bonded slab post-tensioning system

For short cables, prefabrication in the factory and transport on dispenser 2 m x 5.5 m.

Typical, the ducts are transported to site in bundles or packed loose in special transport

frames. Pushing through of individual strands by push-through machine (or by hand for short

cables) before concreting.

For pushing through of the strands after concreting, special care must be taken on the flat

duct to avoid deformation of the duct.

The support of cables is done either with single supports or with support cages. The

distance between tendon supports should be between 0.60 and 1.50 m. The lower limiting value

should be used especially at the high points of the tendon (small radius of curvature). The tendon

are stabilised horizontally and orthogonal reinforcement of plain round bars (diameter 8 mm,

mesh width 1.20 m), fixed directly to the tendon.



Unbonded monostrand system Bonded slab post-tensioning system

Figure 2.46: Transport palette loaded with bundles of monostrands and view of the placed ducts before pushing-

through of the strands

2.4.5 Fire resistance

The minimum concrete cover maintains normally sufficient protection for the post-

tensioning steel [1.3]

. The values can vary according to the standards of the various countries.

2.4.6 Specifications

National and international codes provide a substantial support. Gaps of information can

occur in some special cases. These can be covered with specifications based on different

renowned institutions and technical commissions. The following annex includes an example of

specifications.

References

1.1. BS 8110:Part 2. Structural use of concrete, Sec. 4. Fire resistance, 1985 1.2. CEB-FIP Model Code 1990, Thomas Telford, 1993 1.3. CEB Fire Design of Concrete Structures, July 1991 1.4. prEN 10138-1, prEN 10138-2, prEN 10138-3, cen, 2000 1.5. FIP Design of post-tensioned slabs and foundations, fib, Thomas Telford, May 1998. 1.6. fib Bulletin No. 20 Grouting of tendons in prestressed concrete, 2002. 1.7. FIP Recommendations for the acceptance of post-tensioning systems, June 1993. 1.8. PTI Acceptance Standarts for Post-Tensioning Systems, PTI, Sept. 1998. 1.9. UKCARES REC051PT Model specification for bonded and unbonded post-tensioned flat

slabs, July 2004.

1.10. Brochure VSL 1.11. Brochure DSI DYWIDAG 1.12. Brochure Freyssinet 1.13. Brochure VT Vorspann Technik 1.14. fib Bulletin No. 11 Factory applied corrosion protection of prestressing steel, 2001. 1.15. fib Bulletin No. 15 Durability of post-tensioning tendons, 2001.



Annex: Specification example

1.0 Prestressing steel

Strands in accordance with BS 5896

Strands 0.6

Low Relaxation 2.5 % at 70 % GUTS at 20 C at 1000 hours

Nominal diameter " = 15.2 mm/strands

Nominal area AP = 140.0 mm2/strands

Tensile Strength ftk = 1860 N/mm2

Yield Strength fy = 1670 N/mm2

Youngs modulus EP = 195000 N/mm2

Min. breaking load PN = 260 kN/strand

Duct diameter " = 90 x 20 mm or 70 x 19 mm for slab tendons

Coefficient of friction = 0.25

Unintentional angular deviation k = 0.0012 m-1

Wedge draw-in w = 6 mm

Max. Stressing P0 = 70 % ftk * AP

2.0 Anchorages

2.1 Bearing plates shall be placed perpendicular to the tendon path and shall be shimmed as necessary.

2.2 Grout fittings shall be standard plastic pipe, black and galvanized steel or flexible plastic tubing at

the placers option.

2.3 Additional reinforcement steel required for anchorage block - outs and bursting grids shall be grade

410 unless otherwise noted.

3.0 Tendon fabrication

3.1 Tendon shall be fabricated with sufficient length beyond the bearing plate to allow stressing. A

minimum length of 1.0 m at both ends is required for multistrand stressing.

3.2 Tendon shall be cut to length at the job site from bulk coils. Excessively damaged duct length shall

be removed and replaced completely, not repaired.

3.3 Use of a nylon sling is required to prevent damage to the materials during handling.

3.4 All prestressing coils shall be satisfactorily protected at the job side and when stored off the job site

from corrosion and damage. Sufficient protection shall also be provided for exposed in - place

prestressing steel to prevent excessive deterioration from corrosion.

4.0 Tendon placement

4.1 Strands, ducts and bearing plates according to the quantity and spacing shown on the placing

drawings.

4.2 All vertical profiles shall be measured from the slab soffit to the underside of the tendon duct except

at stressing and dead end anchorages where they measured to the centerline of the anchorage.

4.3 The general contractor shall provide sufficient end form bulk-heads for fastening anchors, attach

bearing plates, and drill forms for extending strands though as required by contract documents. The

general contractor shall provide all necessary shimming required insuring the bearing plates are

placed perpendicular to tendon path.

4.4 Placement of mild steel reinforcement shall be co-ordinated with placement of post-tensioning

tendon. Proper tendon placement has priority.

4.5 Sufficient support steel (size and spacing as indicated on placement drawings) shall be provided.

Maximum spacing of support bars is 1000 mm and minimum " = 16 mm. These bars are used to

prevent lateral and vertical movement of the tendon during concrete placement.



4.6 All support steel and post-tensioning tendons shall be firmly secured in forms to obtain dimension

and locations as shown on placing drawings.

4.7 Concrete shall be placed in such a manner as to insure that alignment of post-tensioning tendons

remains unchanged. Special provision shall be made to insure proper vibration of concrete around

post-tensioning anchorages

4.8 All galvanized duct joints shall be taped

TÀI LIỆU DỰ ỨNG LỰC CỦA FIB

Engineering

Transcript of TÀI LIỆU DỰ ỨNG LỰC CỦA FIB